Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > 0ss | Unicode version |
Description: The null set is a subset of any class. Part of Exercise 1 of [TakeutiZaring] p. 22. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
0ss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | noel 3367 | . . 3 | |
2 | 1 | pm2.21i 635 | . 2 |
3 | 2 | ssriv 3101 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1480 wss 3071 c0 3363 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-dif 3073 df-in 3077 df-ss 3084 df-nul 3364 |
This theorem is referenced by: ss0b 3402 ssdifeq0 3445 sssnr 3680 ssprr 3683 uni0 3763 int0el 3801 0disj 3926 disjx0 3928 tr0 4037 0elpw 4088 exmidsssn 4125 fr0 4273 elnn 4519 rel0 4664 0ima 4899 fun0 5181 f0 5313 oaword1 6367 0domg 6731 nnnninf 7023 exmidfodomrlemim 7057 sum0 11157 ennnfonelemj0 11914 ennnfonelemkh 11925 0opn 12173 baspartn 12217 0cld 12281 ntr0 12303 bdeq0 13065 bj-omtrans 13154 el2oss1o 13188 nninfsellemsuc 13208 |
Copyright terms: Public domain | W3C validator |